Reservoir Computing Using Measurement-Controlled Quantum Dynamics

TL;DR

This paper introduces a quantum RC system that employs the dynamics of a probed atom in a cavity to make fast and reliable forecasts using a small number of artificial neurons compared with the traditional RC algorithm.

Abstract

Physical reservoir computing (RC) is a machine learning algorithm that employs the dynamics of a physical system to forecast highly nonlinear and chaotic phenomena. In this paper, we introduce a quantum RC system that employs the dynamics of a probed atom in a cavity. The atom experiences coherent driving at a particular rate, leading to a measurement-controlled quantum evolution. The proposed quantum reservoir can make fast and reliable forecasts using a small number of artificial neurons compared with the traditional RC algorithm. We theoretically validate the operation of the reservoir, demonstrating its potential to be used in error-tolerant applications, where approximate computing approaches may be used to make feasible forecasts in conditions of limited computational and energy resources.

Figures (9)

• Figure S1: Time evolution of the operator $\langle\sigma_+ \sigma_-\rangle$ for a high (infrequent measurement) and low (frequent measurement) values of $g_z$. Depending on the measurement rate, the system exhibits a Zeno effect with frequent measurements (the orange solid line) or it undergoes oscillations when the measurement rate is low (the blue dashed line).
• Figure S2: Occupation probabilities of Fock states $|n\sigma\rangle \in |00\rangle\dots|21\rangle$ as a function of cavity driving amplitude $\beta$.
• Figure S3: Sketch of the RC system with a measurement-controlled quantum dynamics. The pivotal component of the reservoir is a cavity-atom system with continuously monitored states. The neural activations of the reservoir are given by the Fock states of the atom-cavity quantum system. The reservoir is coherently driven using a signal defined by the discrete points of the input dataset. The classified readouts of the reservoir are processed by means of a linear regression technique.
• Figure S4: (a) Input data generated from a random array representing either a sinusoidal or square waveform. Results of the classification of the sinusoidal and square waveform by the reservoir with (b) 8 and (c) 16 neurons. The target is shown in solid green line and the reservoir prediction in dashed red line.
• Figure S5: The root-mean-square error (RMSE) (the blue square markers) and the accuracy (the red circular markers) obtained for the sinusoidal-square waveform classification task as a function of the number of neurons in the reservoir.